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Global secondary bifurcation, symmetry breaking and period-doubling

Topological Methods in Nonlinear Analysis, 2019
In this paper we provide a criterion for global secondary bifurcation via symmetry breaking. As an application, the occurrence of period-doubling bifurcations for the Lugiato-Lefever equation is proved.
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Multiple Steady States, Limit Cycles and Chaotic Attractors in Evolutionary Games with Logit Dynamics [PDF]

This paper investigates, by means of simple, three and four strategy games, the occurrence of periodic and chaotic behaviour in a smooth version of the Best Response Dynamics, the Logit Dynamics.
Hommes, C.H., Ochea, M.
core

Homoclinic and period-doubling bifurcations for damped systems

Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 1995
We consider the following problem \tag{$P^\alpha$} \begin{cases} ü= −V'(u,t)−\alpha \.{u} \\ u(−∞) = \.{u}(−∞) = 0 = u(∞) = \.{u}(∞) \end{cases} where V\in C^2 (\mathbf R^n × \mathbf R, \mathbf R) is one-periodic
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Investigation on Bifurcation of Map Satisfying Condition of Periodic Doubling Bifurcation

, 2013
In this paper, we consider sufficient conditions for an invariant double circle to occur in a one parameter discrete dynamical systems on a cylinder.
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Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns. [PDF]